+262 Let
\(f(x) = \left\{ \begin{array}{cl} ax+3 & \text{ if }x>0, \\ ab & \text{ if }x=0, \\ bx+c & \text{ if }x<0. \end{array} \right.\)
If f(2)=5, f(0)=5, and f(-2)=-10, and a, b, and c, are nonnegative integers, then what is a+b+c?
+37146 2 is in the first category of x>0
so f(2) = ax+3 a(2) + 3 = 5 then a = 1
0 is in the second category of x = 0
then f(0) would be ab = 5 a, we found is 1 then b = 5
-2 is in the third category x<0
then f(-2) = bx+c =-10 b we found to be 5
5(-2) +c = -10 so c =0
a+b+c=1+5+0=6
